Math Is Fun Forum

evene

Member

Registered: 2015-10-18

Posts: 272

Solving for the unknowns in a diophantine equation

Solve for

in the following:

I didn't really try much due to the sheer ugliness of the system and how intimidating it looks. I want the

to be in "matrix" form. Meaning if $\alpha$ is expressible as

, instead, write

. I have provided an example below:

Example: Find

from the following:

I have found the solutions as

----------

For the example, notice how instead of writing the denominator of each of the unknown as wz-xy or xy-wz, I write it as a matrix

and

respectively.

Last edited by evene (2016-11-02 07:42:03)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving for the unknowns in a diophantine equation

Hi;

Please fix your latex, there is a submit query in the post.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Solving for the unknowns in a diophantine equation

Last edited by evene (2016-11-02 09:39:13)

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,432

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Re: Solving for the unknowns in a diophantine equation

I assume you mean the determinant of those matrices -- division by a matrix is not defined.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Solving for the unknowns in a diophantine equation

Sure.. determinant...

Why is division by a matrix not defined? Isn't a matrix simply subtracting values, given the fact that the elements of the matrix can never all equal 0...

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,432

Website

Re: Solving for the unknowns in a diophantine equation

Why is division by a matrix not defined?

Firstly, matrices are not numbers: if we want to define "division" amongst them, then we use the matrix inverse (the same goes for other algebraic objects, like operators). However, matrix multiplication is in general not commutative: given any two matrices A and B, it is not true that AB = BA. Therefore, if you want to "divide by a matrix", you need to distinguish between multiplying the left by the inverse or the right by the inverse.

Isn't a matrix simply subtracting values

No. Perhaps you are getting mixed up with the determinant, which is a different concept.

given the fact that the elements of the matrix can never all equal 0...

Sure, elements of a matrix can all be 0. It won't be invertible, but it's still a matrix. (It is appropriately named the zero matrix.)